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Practice Class 9 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn coefficients, degree of polynomial, polynomial values, algebraic expressions, and zeros of polynomials with detailed solutions for CBSE board exams.
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Chapter Information
Subject: Mathematics
Class: 9
Chapter: Polynomials
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction:
Polynomials are algebraic expressions consisting of variables, coefficients, constants, and exponents. They are a key part of algebra and help students understand mathematical relationships, equations, and patterns. Mastering polynomials builds a strong foundation for higher-level mathematics.
What You Will Learn?
✔ Coefficients and Constants
✔ Degree of Polynomial
✔ Polynomial Values
✔ Monomials, Binomials and Trinomials
✔ Zeros of Polynomials
✔ Algebraic Expressions
✔ Polynomial Classification
✔ Board Exam Preparation
Why This Topic Is Important?
Polynomials are used in algebra, coordinate geometry, and many advanced mathematical topics. Understanding polynomial concepts improves analytical thinking and helps students solve complex mathematical problems effectively.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. What is the coefficient of
$$x$$
in the polynomial
$$6x^4-8x^2+13x-9$$
A)
$$6$$
B)
$$8$$
C)
$$13$$
D)
$$9$$
Answer:
$$13$$
Useful Formula for this Question:
The coefficient is the numerical factor attached to a variable term.
Concept Behind This Question:
Students should identify the coefficient corresponding to the required variable term.
Step-by-Step Solution:
Given polynomial:
$$6x^4-8x^2+13x-9$$
The term containing
$$x$$
is:
$$13x$$
Therefore, the coefficient of
$$x$$
is:
$$13$$
Hence, the correct answer is:
$$13$$
Exam Tip:
Look only at the term containing the specified variable.
Q2. Which of the following is a trinomial?
A)
$$5x^3$$
B)
$$x+8$$
C)
$$x^2+5x+6$$
D)
$$11$$
Answer:
$$x^2+5x+6$$
Useful Formula for this Question:
A trinomial contains exactly three terms.
Concept Behind This Question:
Students should classify polynomials based on the number of terms.
Step-by-Step Solution:
$$5x^3$$
contains
$$1$$
term.
$$x+8$$
contains
$$2$$
terms.
$$x^2+5x+6$$
contains
$$3$$
terms.
$$11$$
contains
$$1$$
term.
Therefore:
$$x^2+5x+6$$
is a trinomial.
Hence, the correct answer is:
$$x^2+5x+6$$
Exam Tip:
Count the terms separated by plus or minus signs.
Q3. Find the value of
$$p(x)=4x^2+3x+2$$
when
$$x=5$$
A)
$$112$$
B)
$$117$$
C)
$$120$$
D)
$$125$$
Answer:
$$117$$
Useful Formula for this Question:
Substitute the given value of
$$x$$
into the polynomial.
Concept Behind This Question:
Students should evaluate polynomial expressions accurately.
Step-by-Step Solution:
Given:
$$p(x)=4x^2+3x+2$$
Substitute:
$$x=5$$
$$p(5)=4(5)^2+3(5)+2$$
$$=4(25)+15+2$$
$$=100+15+2$$
$$=117$$
Therefore, the correct answer is:
$$117$$
Exam Tip:
Always calculate powers before multiplication and addition.
Q4. What is the degree of the polynomial
$$12x^{15}+7x^5-4x+10$$
A)
$$5$$
B)
$$12$$
C)
$$15$$
D)
$$10$$
Answer:
$$15$$
Useful Formula for this Question:
The degree of a polynomial is the highest exponent of the variable.
Concept Behind This Question:
Students should identify the largest power present in the polynomial.
Step-by-Step Solution:
The powers of
$$x$$
are:
$$15,;5,;1,;0$$
The highest power is:
$$15$$
Therefore:
Degree
$$=15$$
Hence, the correct answer is:
$$15$$
Exam Tip:
Ignore coefficients while determining the degree.
Q5. If
$$p(x)=x-42$$
then the zero of the polynomial is:
A)
$$42$$
B)
$$-42$$
C)
$$0$$
D)
$$4$$
Answer:
$$42$$
Useful Formula for this Question:
A zero of a polynomial satisfies:
$$p(x)=0$$
Concept Behind This Question:
Students should determine the value of
$$x$$
that makes the polynomial equal to zero.
Step-by-Step Solution:
Given:
$$p(x)=x-42$$
For zero:
$$x-42=0$$
$$x=42$$
Therefore:
The zero of the polynomial is
$$42$$
Hence, the correct answer is:
$$42$$
Exam Tip:
Set the polynomial equal to zero and solve carefully.
Important Formulas & Concepts
1. Coefficient
The numerical factor attached to a variable.
Example:
$$9x^3$$
Coefficient:
$$9$$
2. Constant Term
The term without a variable.
Example:
In
$$5x^2+7x+12$$
the constant term is:
$$12$$
3. Degree of a Polynomial
The highest exponent of the variable present in the polynomial.
4. Monomial, Binomial and Trinomial
Monomial:
$$7x^4$$
Binomial:
$$x+10$$
Trinomial:
$$x^2+4x+5$$
5. Zero of a Polynomial
If
$$p(a)=0$$
then
$$a$$
is called a zero of the polynomial.
FAQs
1. What is a coefficient?
The numerical factor attached to a variable.
2. What is a trinomial?
A polynomial containing exactly three terms.
3. What is the degree of a polynomial?
The highest exponent of the variable.
4. How do we evaluate a polynomial?
By substituting the given value of the variable.
5. What is a zero of a polynomial?
The value that makes the polynomial equal to zero.
Common Mistakes
❌ Confusing coefficients with exponents.
❌ Counting terms incorrectly.
❌ Ignoring the highest exponent while finding degree.
❌ Making calculation errors during substitution.
❌ Forgetting sign changes while solving for zeros.
Quick Revision Notes
✔ Coefficient = Numerical factor.
✔ Constant term = No variable.
✔ Monomial = One term.
✔ Binomial = Two terms.
✔ Trinomial = Three terms.
✔ Degree = Highest exponent.
✔ Zero of polynomial means:
$$p(x)=0$$
✔ Use BODMAS while evaluating expressions.
Conclusion
Polynomials are a fundamental part of Class 9 Mathematics and form the basis for many advanced algebraic concepts. Understanding coefficients, degrees, values, and zeros of polynomials helps students solve problems efficiently and perform well in examinations. Regular MCQ practice strengthens conceptual understanding and improves confidence.
Related Links
- Class 9 Maths Chapter 2 Polynomials part 11
- Class9 Maths Chapter2 Polynomials part 10
- Class 9 Maths Chapter 2 Polynomials – Part 9
- Class 9 Maths Chapter 2 Polynomials degree of polynomial – Part 8
- Class 9 Maths Chapter 2 Polynomials – Part 7
- Class 9 Maths Chapter 2 Polynomials degree of polynomial – Part 6
- Class 9 Maths Chapter 2 Polynomials coefficients MCQ – Part 5
- Class 9 Maths Chapter 2 Polynomials, value of polynomials – Part 4
- Class 9 Maths Chapter 2 Polynomials constant polynomial – Part 3
- Class 9 Maths Chapter 2 Polynomials MCQ with solutuins – Part 2
- Class 9 Maths Chapter 1 Number Systems, irrational numbers
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